Terrance Tomkow at Tomkow.com:
…the question, What are the laws of nature? may be stated thus: What are the fewest and simplest assumptions, which being granted, the whole existing order of nature would result? Another mode of stating it would be thus: What are the fewest general propositions from which all the uniformities which exist in the universe might be deductively inferred? J.S.Mill, 1843•
… if we knew everything, we should still want to systematize our knowledge as a deductive system, and the general axioms in that system would be the fundamental laws of nature” Frank Ramsey, 1928•
“a contingent generalization is a law of nature if and only if it appears as a theorem (or axiom) in each of the true deductive systems that achieves a best combination of simplicity and strength” David Lewis 1973 •
Vereshchagin & Vitányi,2004•
The quotes from Mill, Ramsey and Lewis above express the what philosphers call the “ Best System Analysis” of Laws.
BSA is probably the most widely accepted answer we have to the question, “What is it to be a Law of nature?” Even so, it is notoriously fraught with unanswered questions. A short list:
Can the account properly distinguish accidental from nomological regularities?
Can it explain the connection between the laws of nature, counterfactuals and dispositions?
Why should we count only generalizations as laws, given that many scientific principles do not obviously take this form? Can't singular statements describing, say, fundamental constants be laws too?
What is the connection between this deductive account of laws and our inductive methods of discovering them?
How does BSA accommodate the existence of probabilistic laws?
What do Mill and Lewis mean when they speak of “simplicity”? Isn't simplicity in the eye of the beholder? If so how can it be a subjective matter what the laws of nature are? Or, if simplicity is just a measure of shortness of our sentences, doesn't that make law-hood a matter of what language we happen to speak?
And, anyway, why should we think that the laws of nature must be simple in any sense?
In this post I want to raise different and, I think, more fundamental problems for BSA and provide an alternative theory of lawhood based on Algorithmic Information Theory (AIT). This new theory is precisely captured in the theorem of AIT that appears above. Don't worry if you don't understand it just now. AIT is a recent development and a novelty to most philosophers. Before we are done, I hope to have explained to you what this equation means and to have convinced you of its deep significance.
More here.